"Suppose that those classes, from elementary school right through to high school, amounted to nothing more than reading dictionaries, getting drilled in spelling and formal grammatical construction, and memorizing vast vocabulary lists -- you never read a novel, nor a poem; never had contact with anything beyond the pedantic complexity of English spelling and formal grammar, and precise definitions for an endless array of words. You would probably hate the subject."

This is a great point, and the post goes on to talk about why it's not just a lack of "real world" examples that makes math and science such boring, intimidating subjects.Â Here's the perfect example of how a real world example definitely did not help one student with physics:
[youtube]cIIwwCi2zwk[/youtube]
So if memorizing facts and formulas is no use, and contrived, often bizarre examples are no help, how should we teach math and science?
I'm not sure I have any great insights, but I can give you three examples of what has worked for me.
First, I think it helps to have (or to project to your students) an attitude that allows for the real value and usefulness of science and math.Â This does not mean that great teachers and students have to be died-in-the-wool atheists or materialists.Â But I do think there are some basic ideas without which science and math will never be meaningful or interesting:
1.Â The world is more complicated than it might seem;
2.Â We can figure out the way it works;
3.Â We can put the knowledge to use.
As Richard Feynman explained:

"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled."

Doing some googling to uncover the source of the quote leads me to a post on Edward Tufte's homepage, Grand truths about human behavior.Â There you'll find a collection of quotes that express this notion better than I can.
Second, you cannot study physics, geometry, biology, or any similar subject in isolation.Â When I was in high school a lot of the stuff we went over in math class junior year didn't make sense until I took physics senior year.Â In college I took calculus I and II as a computer science student and did fairly well, but I forgot everything I had read the day after each final exam.Â When I took discrete math, though, the class was so much more interesting because I could see how it applied to CS.
Finally, one great way to teach science is through storytelling.Â This is a case where extensive Bible study might be perfect preparation for giving a science lecture - Jesus knew 2000 years ago that parables were much more effective teaching tools than lists of facts and figures (or commandments).
The facts of the story are not nearly as important as the lesson and the exercise in creative thinking.Â One great example of this is The Physics of Superheros by James Kakalios.Â This is a great book - the author talks about the origin stories and powers of various super heroes and uses these very fictional examples to illustrate real physics.Â He does not do so by brutally criticizing Stan Lee and insulting Superman.Â Instead he uses the "miracle exception" to the laws of physics represented by each super power to tell a story about how the world really works.
Thanks to The Adventures of the Accordion Guy for pointing out the post on teaching math like English.